Geodesic
The curvature of contact structures on 3–manifolds
Krouglov, Vladimir1
1Department of Geometry, Institute for Low Temperature Physics and Engineering, 47 Lenin Ave, Kharkov 61103, Ukraine
Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1567-1579
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We study the sectional curvature of plane distributions on 3–manifolds. We show that if a distribution is a contact structure it is easy to manipulate its curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed 3–dimensional manifold, there is a metric such that the sectional curvature of the contact distribution is equal to − 1. We also introduce the notion of Gaussian curvature of the plane distribution. For this notion of curvature we get similar results.

DOI : 10.2140/agt.2008.8.1567
Keywords: contact structure, uniformization, curvature

Krouglov, Vladimir  1

1 Department of Geometry, Institute for Low Temperature Physics and Engineering, 47 Lenin Ave, Kharkov 61103, Ukraine 
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Krouglov, Vladimir. The curvature of contact structures on 3–manifolds. Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1567-1579. doi: 10.2140/agt.2008.8.1567

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